Binomial Option Pricing Model

The model was developed by John Cox, Stephen Ross and Mark Rubinstein in 1979. It breaks the time until expiry into steps. At each step, the price moves either up or down. The option’s value is calculated at the end of the tree and then worked backwards to today, using probabilities that make the calculation consistent with a risk-free return.

For a simple one-step example, a share trades at 100 and will be either 120 or 80 next period, with interest rates of zero. A call option with an exercise price of 100 would be worth 20 if the share rises and nothing if it falls. The model’s risk-neutral probability of a rise is 50%, so the option is worth 50% of 20, or 10, today.

With many small steps, the binomial model’s results approach those of the Black-Scholes model.

Its main advantage is flexibility. It can value American options, which can be exercised early, and options with more complex features, which the basic Black-Scholes formula cannot handle.